Monotonicity of expected $f$-vectors for projections of regular polytopes
نویسندگان
چکیده
منابع مشابه
The monotonicity of f-vectors of random polytopes
Let K be a compact convex body in R, let Kn be the convex hull of n points chosen uniformly and independently in K, and let fipKnq denote the number of i-dimensional faces of Kn. We show that for planar convex sets, Erf0pKnqs is increasing in n. In dimension d ě 3 we prove that if limnÑ8 Erfd ́1pKnqs An “ 1 for some constants A and c ą 0 then the function n ÞÑ Erfd ́1pKnqs is increasing for n lar...
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Let K be a compact convex body in R, let Kn be the convex hull of n points chosen uniformly and independently in K, and let fipKnq denote the number of i-dimensional faces of Kn. We show that for planar convex sets, Erf0pKnqs is increasing in n. In dimension d ě 3 we prove that if limnÑ8 Erfd ́1pKnqs Anc “ 1 for some constants A and c ą 0 then the function n ÞÑ Erfd ́1pKnqs is increasing for n la...
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Let K be a compact convex body in R, let Kn be the convex hull of n points chosen uniformly and independently in K, and let fipKnq denote the number of i-dimensional faces of Kn. We show that for planar convex sets, Erf0pKnqs is increasing in n. In dimension d ě 3 we prove that if limnÑ8 Erfd ́1pKnqs An “ 1 for some constants A and c ą 0 then the function n ÞÑ Erfd ́1pKnqs is increasing for n lar...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2017
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13827